Question: Solve for $x$ and $y$ using elimination. ${-5x-3y = -32}$ ${3x-3y = -24}$
We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $-1$ ${5x+3y = 32}$ $3x-3y = -24$ Add the top and bottom equations together. $8x = 8$ $\dfrac{8x}{{8}} = \dfrac{8}{{8}}$ ${x = 1}$ Now that you know ${x = 1}$ , plug it back into $\thinspace {-5x-3y = -32}\thinspace$ to find $y$ ${-5}{(1)}{ - 3y = -32}$ $-5-3y = -32$ $-5{+5} - 3y = -32{+5}$ $-3y = -27$ $\dfrac{-3y}{{-3}} = \dfrac{-27}{{-3}}$ ${y = 9}$ You can also plug ${x = 1}$ into $\thinspace {3x-3y = -24}\thinspace$ and get the same answer for $y$ : ${3}{(1)}{ - 3y = -24}$ ${y = 9}$